Diffusive Flux Surface Area

Gas-liquid mass transfer is often rate-limiting for gases that are sparingly soluble in the broth, such as oxygen and methane. Although highly soluble, carbon dioxide exhibits pH-dependent partitioning between gaseous and dissolved forms (CO2, H2CO3, HCO—, CO|-) that is influenced by the rates of both reaction and mass transfer. Proper interpretation of the respiratory coefficient (RQ) in fermentations operated at neutral pH requires consideration of CO2 dynamics. The OTR has already been used to determine the productivity limit of a CSTR used for biomass production in equation 12. In general, the rate of mass transfer from the gas to the liquid phase is given as

where NA is the rate of gas transfer (mmol/l x h) and the remaining terms have the same definitions as in equation

12. For sparged, agitated tanks, kLa has typical values in the range from 50 to 1,400 h-1. Several correlations have been developed for kLa as a function of the gassed power input per unit volume and the superficial gas velocity for Newtonian broths in a variety of fermentors (43). The correlations can offer wide variability in mass transfer estimates and should be used in conjunction with knowledge from past experience or empirical measurements of kLa

(e.g., dynamic or sulfite oxidation methods). Oxygen transfer to shear-sensitive mammalian cells requires gentle agitation combined with surface or membrane aeration, or light sparging, as opposed to the large power inputs and high rates of gas sparging in microbial fermentations. This limitation is somewhat offset by the fact that mammalian cells have lower O2 requirements (0.05 to 0.5 mmol/

109 cells x h) (44) and grow to lower cell densities (106 to 107 cells/mL) than microbial cultures.

VARIATIONS ON THE SINGLE CSTR Single CSTR with Recycle

Volumetric productivity is related to the concentration of active catalyst. Cell or enzyme concentrations greater than the steady state obtained from the simple CSTR can be achieved by separating cells from the effluent stream and recycling them to the vessel (27,45) or by retaining them within reactor. Higher catalyst concentrations enhance substrate conversion and reduce the reactor size necessary to attain a given conversion. Recycle operation improves system stability in the face of feed disturbances by retaining cells in the vessel even under conditions that would cause washout in the simple CSTR. Recycle systems can be operated at dilution rates, or throughputs, greater than the specific growth rate of the organism. Productivity improvements achieved with cell recycle are demonstrated in Table 4 for Saccharomyces cerevisiae ATCC 4126 and Zym-omonas mobilis ATCC 10988 at 100 g/L glucose feed.

Cell Recycle Methods. Cell recycle is implemented through a cell separation step, often by a unit operation commonly used in the initial stages of downstream processing. Typical methods of continuous cell separation include centrifugation, filtration, and sedimentation. Cell separation can be viewed as having two often equally important purposes: (7) the recovery or retention of cells for reuse and (2) the removal of potentially inhibitory byproducts or products from the culture environment. The separation step often has to satisfy additional performance requirements such as handling of shear- or temperature-sensitive materials, selectivity in rejection or recovery, containment, maintenance of asepsis, corrosion resistance, brief retention time, and ease of cleaning, sterilization, maintenance, and validation. Recycle operation is standard for reactors using stable enzymes, because discarding expensive active catalyst is economically unfeasible. Cell separation operations are discussed elsewhere in the context of downstream processing, although a brief description is presented here in relation to cell recycle.

Sedimentation. Sedimentation is the settling of particles in a gravitational field. With low energy requirements and simple equipment, sedimentation is a relatively inexpensive way of separating a dilute cell phase. Waste treatment is by far the largest application of sedimentation-based cell recycle, in which cells are typically separated in large sedimentation tanks using lime or clay to enhance flocculant formation. The settling velocity (u0) for an isolated spherical particle can be described using Stoke's law:

fluid density, g is the gravitational acceleration constant, and g is the fluid viscosity. The functional dependence of Stoke's law suggests ways of increasing the settling velocity. The easiest and most common method is to increase the effective cell size by promoting flocculation (cell aggregation) through physiological, chemical, and physical factors: selection of flocculant strains; modification of cell wall structure or surface charge; changing the pH, temperature, or shear stress; addition of inorganic salts (e.g., Ca2 + and Mg2 + salts) or clays; controlling the concentration of certain nutrients or products (e.g., extracellular polysaccharides); and controlling the cell age or growth phase. Selective cell recycle has been implemented using the differential sedimentation properties of a desired and unwanted microorganism (34-36). The properties of a particular broth are generally unchangeable and will probably only impede particle settling.

Although equation 40 holds for dilute suspensions of cells, the interactions among settling particles in concentrated slurries results in hindered settling. The hindered particle velocity (uh) is influenced by the particle concentration and can be expressed with the following correlation (49):

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